Whether or not I would take on a client I hate would depend largely on what kind of service I was providing to the customer. If I was merely providing a service where minimal contact/communication is necessary, and I can just get on and provide the service, I dare so i'd have no problem with that.

In the area of web design / development, however, where communication and understanding is key to helping the customer achieve their goals, I doubt I would be prepared to take that customer on - not simply because I hate them, though. If I felt my hatred for that customer would hinder my ability to communicate with them properly (and perhaps increase the risk of the project failing to produce the results the client hoped for), I would consider turning that customer away.

I would prefer to turn away some business, then take someone on with whom I have a sloppy relationship, disappoint and fail them, and ruin my reputation.

At the end of the day though - if you we are talking in terms of us hating the customer (and the customer not having any hatred for us), I guess we should just try and be mature and professional about things, and not let it get in the way of the project.